hey i have a question about a limit problem. i tried putting values less than 0 i.e. .1, .01, .001...and so on but it didnt seem to work...help?
lim as x-->theta of theta/tan(4theta)
thanks...
Try this:
$\displaystyle \lim_{\theta \to 0}\frac{\theta}{tan(4\theta)}$
Change the variable to $\displaystyle \alpha = 4 \theta$. Then $\displaystyle \alpha \to 0$ as $\displaystyle \theta \to 0$. Thus
$\displaystyle \lim_{\theta \to 0}\frac{\theta}{tan(4\theta)} = \lim_{\alpha \to 0}\frac{\frac{1}{4} \alpha}{tan(\alpha)} = \frac{1}{4} \cdot
\lim_{\alpha \to 0}\frac{\alpha}{tan(\alpha)}$
Does this help?
-Dan